general maths Q's (1 Viewer)

[hsc100]

Can anyone plz help me with these questions.Thanx

1.From 5 students each of whose names has been written on a card in a hat, 2 are to be chosen at random for a job.the pobability that one particualr student is chosen is?

2.a jar contains 5cents, 20 c and $2.if i take out 2 coins together at andom, the probability of the total value of the coins being $2.05 is?


3.a cricketer can, on average, catch 1 in 3 chances.if 2 balls are hit to him, the probabiliy that he will catch one and drop one is?

4.the probability of a man aged 102 dying in the oming 12 months is 0.21.the probability of a man aged 103 dying in the coming 12 months is 0.25.the probability of a 102 year old man being alive in 2 years time is therefore closest to


5.to decide who has first turn in a game, alana and bruce toss a coin in turn until one of them tosses a tail.if alana tosses first, the probability before tossin begins that she will win with her second toss is?

6.6 people at a meeting are to be seated at a round table.if the chair of the meeting must sit on one particular chair, the number of diferent ways the meeting may be seated is?

7.At a party, 6 boys are to be matched with 6 girls by drawing a girls name from one hat and a boys name from another hat.The probability that Cathy will be matched with Con is?

8.A normal pack of 52 cards is shuffled.two cards are selected at random without replacements.what is the probability that one of them is the 6 of hearts.

9.there are 15 milk chocalates, 10 dark and 5 lolliesin a jar.two itemsfrom the jar are selected at random without replacement.Whats the probability of selecting

a) no milk chocolates
b)at least one dark chocolate


10. a man has 4 pairs of socks in a drawer each pair a different colour.if he selects 2 socks randomly what is the probability that they are a matching pair?

 

[duckcowhybrid]

For all of them just draw a tree diagram and on each branch label the possible outcomes. I can't draw them up here, but once you draw a diagrama and on each branch there is one outcome follow by a 2nd outcome and so on you should get it pretty easy by reading the diagram and counting the fractions.

 

[PC]

As previously stated, a tree diagram is most useful here. It's a very visual means of making sure every possibility is counted. With lots of practice, a tree diagram isn't vital.

1.From 5 students each of whose names has been written on a card in a hat, 2 are to be chosen at random for a job.the pobability that one particualr student is chosen is?

The student is either chosen first, or chosen second.
P(first) = 1/5
P(second) = 4/5 x 1/4 = 1/5
.: P(chosen) = 1/5 + 1/5 = 2/5

2.a jar contains 5cents, 20 c and $2.if i take out 2 coins together at andom, the probability of the total value of the coins being $2.05 is?

This is tough without a count of the number of each coin in the jar. Let's assume there is only one of each coin in the jar. That means the 5¢ coin and the $2 coin must be selected.
.: P($2.05) = P($2 then 5¢) + P(5¢ then $2)
= 1/3 x 1/2 + 1/3 x 1/2
= 1/3

3.a cricketer can, on average, catch 1 in 3 chances.if 2 balls are hit to him, the probabiliy that he will catch one and drop one is?

P(one of each) = P(catch first, drop second) + P(drop first, catch second)
= 1/3 x 2/3 + 2/3 x 1/3
= 4/9

Note that we don't reduce the denominator here. It's not a physical count of catches but an overall average based on many previous results.

4.the probability of a man aged 102 dying in the oming 12 months is 0.21.the probability of a man aged 103 dying in the coming 12 months is 0.25.the probability of a 102 year old man being alive in 2 years time is therefore closest to

P(102 year old living 2 years) = (1 – 0.21) x (1 –*0.25)
= 0.5925
= 237/400

5.to decide who has first turn in a game, alana and bruce toss a coin in turn until one of them tosses a tail.if alana tosses first, the probability before tossin begins that she will win with her second toss is?

P(Alana wins with 2nd toss) = P(Alana heads, Bruce heads, Alana tails)
= 1/2 x 1/2 x 1/2
= 1/8

6.6 people at a meeting are to be seated at a round table.if the chair of the meeting must sit on one particular chair, the number of diferent ways the meeting may be seated is?

Number of ways = 1 x 5 x 4 x 3 x 2 x 1
= 120

7.At a party, 6 boys are to be matched with 6 girls by drawing a girls name from one hat and a boys name from another hat.The probability that Cathy will be matched with Con is?

Cathy will get paired with a boy, and there is a 1/6 chance of it being Con.

8.A normal pack of 52 cards is shuffled.two cards are selected at random without replacements.what is the probability that one of them is the 6 of hearts.

P(6H) = P(6H first) + P(6H second)
= 1/52 + 51/52 x 1/51
= 1/26

9.there are 15 milk chocalates, 10 dark and 5 lolliesin a jar.two itemsfrom the jar are selected at random without replacement.Whats the probability of selecting
a) no milk chocolates
b)at least one dark chocolate

(a) P(no milk chocolates) = P(DD) + P(DL) + P(LD) + P(LL)
= (10/30 x 9/29) + (10/30 x 5/29) + (5/30 x 10/29) + (5/30 x 4/29)
= 7/29

(b) P(at least one dark chocolate) = 1 – P(no dark chocolates)
= 1 – [P(MM) + P(ML) + P(LM) + P(LL)]
= 1 – [(15/30 x 14/29) + (15/30 x 5/29) + (5/30 x 15/29) + (5/30 x 4/29)]
= 1 – 38/87
= 49/87

10. a man has 4 pairs of socks in a drawer each pair a different colour.if he selects 2 socks randomly what is the probability that they are a matching pair?

The man has 8 socks in the drawer. He will choose a sock to start with. This leaves 7 socks in the drawer, and only one will be a matching sock.
.: P(matching pair) = 1/7

 

[hsc100]

Thanks so much for your answer.