Bunch of Mixed Probability (1 Viewer)

[Makro]

9. Two dice are rolled and two coins are tossed. Find the probability of getting:
b) A head, a tail and a total of 8

I did P(HT) x P(TH) x P (total of 8)
= 1/4 x 1/4 x 1/6

Correct Answer: 5/72

My logic was there were 6 pairs of numbers that could make up 8, hence 6/36. Can anyone explain this to me, please? I don't do well with probability.

 

[Makro]

Thanks, so the whole total of 8 thing is pure logic? It's weird even with the explanation.

 

[Drongoski]

I did P(HT) x P(TH) x P (total of 8)
= 1/4 x 1/4 x 1/6

Correct Answer: 5/72

My logic was there were 6 pairs of numbers that could make up 8, hence 6/36. Can anyone explain this to me, please? I don't do well with probability.

P(a H & a T) = P(HT or TH) = 1/2
P(a total of 8) = P[ a (2,6), a (6,2), a (3,5), a (5,3) or a (4,4)] = 5 out of 6 x 6 = 36
equally likely outcomes = 5/ 36

Therefore required prob = 1/2 x 5/36 = 5/72

I hope this explains more clearly for you

 

[Makro]

That approach makes more sense. I counted 4,4 twice so hmm. Thanks.

 

[Makro]

18. A card is chosen at random from a set of 10 cards numbered 1 to 10. A second card is chosen from a set of 20 cards numbered 1 to 20. Find the probability that the number these cards make is:
a) 911
b) less than 100
c) between 300 and 500

A + B are done. I got a) 1/200 and b) 81/200.

c) I did 2/10 x 9/20 = 9/100.

Answers: 11/100.

Explanation if you can, please. Thank you.

 

[Makro]

Sorry for the tripler, last question from this review.

Two cards are chosen at random from a deck of 52 cards. Find the probability of choosing:
a) 2 aces
b) 2 red cards
c) a heart and a diamond
d) a 10 and a 5

a) and b) i've done.

c) I tried doing 1/13 * 13/51 = 1/51

with d) I ended up with the same thing.

Answers are: c) 13/102 d) 8/663

 

[Timothy.Siu]

A + B are done. I got a) 1/200 and b) 81/200.

c) I did 2/10 x 9/20 = 9/100.

Answers: 11/100.

Explanation if you can, please. Thank you.

well, to be between 300 and 500, the card from 1-10 has to be 3 or 4
so theres a 2/10 chance of that, but to make a number between that, the second card chosen has to be a 2 digit number, 11/20

so 2/10 x11/20=11/100

 

[Makro]

d) 26/52 * 13/51

the first card is 26/52 since it can be a heart OR diamond

d) 8/52 * 4/51

same principle

First one out of those two was 26/52 * 25/51 which I ended up getting because of the explanation.

for d), I don't understand why it's that. if there are 4 10s and 4 5s, shouldn't it be 8/52 * 7/51?

well, to be between 300 and 500, the card from 1-10 has to be 3 or 4
so theres a 2/10 chance of that, but to make a number between that, the second card chosen has to be a 2 digit number, 11/20

so 2/10 x11/20=11/100

Thanks I got the first part just didn't get my head around the 2nd bit