Probability (1 Viewer)

[Petinga]

1. Consider 2 spin dials. On one of them the letters A, B, C, D and E are printed, and, on the other, the digits 1,2,3,4,5. When the dials are spun, it is equally likely thatthey will stopon any letter/number.
What is probabily:
- B and even number
- cor D abd an odd number
-E and a eveb number or c and a number greater then 3
-a conosnat and odd numberor a conosnat and number greater than 2

2. A die is tossed 3 times. What is probabiolty:
a) 3 sixes
b) 0 sixes
c)3 odd nmbers
d)3 even numbers
e) a 6 in first two tossesonly
f) a six, not a six, a six , in that order

3. One un contains 2 red cubes and 4 blue cubes and a second urn contains 4 red cubes and 3 blue cubes. One cube is selected at random from each of the two urns. Ehat is the probabiliy that one cube is ed?

4. A man finds that he is late for work on 10 per cent of occasions if he is on time the previeous day and 20 per cent of occcison if he is late the previous day. Givene he was on rime on monday, what is the probbilty that he is on time on wednesday?

5. To open a locked safe requires a correct 3 digit combinbationb. Calcultae the probbilty of:
a) succeddin at first attemot
b) failing at first attempt

 

[Riviet]

1. Consider 2 spin dials. On one of them the letters A, B, C, D and E are printed, and, on the other, the digits 1,2,3,4,5. When the dials are spun, it is equally likely thatthey will stopon any letter/number.
What is probabily:
- B and even number
- C or D and an odd number
-E and a even number or c and a number greater then 3
-a consonant and an odd number or a consonant and a number greater than 2

Please be a little more careful when you type, you have a number of typos.

P(B and even number)=1/5x1/5 + 1/5x1/5
=2/25

P(C/D and odd number)=2[1/5x1/5 + 1/5x1/5 + 1/5x1/5]
=6/25

P(E and a even number or c and a number greater then 3)=P(E and a even number) + P(c and a number greater then 3)
=2/25 + [1/5x1/5 + 1/5x1/5)
=4/25

P(a consonant and an odd number or a consonant and a number greater than 2)=P(a consonant and an odd number)j + P(a consonant and a number greater than 2)
=3(1/5x1/5 + 1/5x1/5 + 1/5x1/5) + 3(1/5x1/5 + 1/5x1/5 + 1/5x1/5)
=6(3/25)
=18/25

 

[Riviet]

2. A die is tossed 3 times. What is probabiolty:
a) 3 sixes
b) 0 sixes
c)3 odd nmbers
d)3 even numbers
e) a 6 in first two tossesonly
f) a six, not a six, a six , in that order

Total number of possible outcomes=6³=216

a) P(3 sixes)= 1/6 x 1/6 x 1/6
=1/216

b) P(0 sixes)= 5/6 x 5/6 x 5/6
=125/216

c) P(3 odd numbers)= 1/2 x 1/2 x 1/2
=1/8

d) P(3 even numbers)= P(3 odd numbers)
=1/8

e) Assuming it means only 6's tossed in first two tosses:
P(6 in first two tosses only)= 1/6 x 1/6 x 5/6
=5/216

OR assuming if it means that a six can't be tossed in third but any number in first 2 tosses:
P(6 in first two tosses only)= 1 x 1 x 5/6
=5/6

f) P(a six, not a six, a six , in that order)= 1/6 x 5/6 x 1/6
=5/216

 

[Riviet]

3. One un contains 2 red cubes and 4 blue cubes and a second urn contains 4 red cubes and 3 blue cubes. One cube is selected at random from each of the two urns. Ehat is the probabiliy that one cube is ed?

un=urn? Lol, i'm guessing it's a container from its context.
P(Red from first or Red from second)= 2/6 + 4/7
=19/21 , assuming that you mean that it is red from at least one of the two selected.

4. A man finds that he is late for work on 10 per cent of occasions if he is on time the previeous day and 20 per cent of occcison if he is late the previous day. Givene he was on rime on monday, what is the probbilty that he is on time on wednesday?

Draw the tree diagram, and label the stems with the respective probabilities as fractions. Since he is ontime on Monday, we only take the large branch connected to "monday ontime". From the "monday ontime" branch, draw two sub-branches label them "late" and "on time". Now using the info, label the stem for "late" with 1/10 and the stem for "on time" with 9/10. Using all the given info again, we repeat this step for the "late" and "on time" sub-branches, making sure each sub-branch adds up to 1 i.e 1/10+9/10=1 and 4/5+1/5=1

Using the diagram find all the possible roots along the tree and add up their probabilities:

.: P(on time on Wednesday)= 9/10x9/10 + 1/10x4/5
=89/100

 

[Riviet]

5. To open a locked safe requires a correct 3 digit combinbationb. Calcultae the probbilty of:
a) succeddin at first attemot
b) failing at first attempt

The possibe digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, ten in total.
Therefore number of possible conbinations= 1/10 x 1/10 x 1/10 = 1/1000

a) .: P(correct on first attempt)= 1/10 x 1/10 x 1/10 =1/1000

b) P(failing on first attempt) = 1 - P(correct on first attempt)
=1 - 1/1000
=999/1000