Probability Questions?

Question

Hi I was really struggling with these 2 questions in pariticular and appreciate any help, if you could also explain how you work it out would be great.

1. Card is drawn at random from pack of 52 playing cards. Card is replaced and a 2nd is drawn. Card is replaced and 3rd is drawn. What is probability of drawing:

A- three hearts (I got 1/64? )
b- at least 2 hearts (10/64? )
c- exactly one heart

2.A bag contains 6 red marbles and 4 blue marbles. A marble is drawn at random and not replaced. Two further draws are made, again without replacement. Find the probability of drawing:

A) 3 red marbles
B) 3 blue marbles
C) no red marbles 
D) at least 1 red marble

Thank you :)

hayharbr · Answer

1A I agree (1/4 • 1/4 • 1/4) and B too (3 • 3/64 + 1/64)
and since no hearts is 3/4 • 3/4 • 3/4 = 27/64, exactly one heart would be 1 - (P(at least two) + P(none))
= 1 - (10/64 + 27/64)
= 1 - 37/64
= 27/64

Or get it directly; P(h not h not h) = 1/4 • 3/4 • 3/4 = 9/64 and the same for P(not h h not h)
and P(not h not h h) so 3 • 9/64 = 27/64

And you'd do #2 the same way except without replacement, and the probabilities aren't 1/4 & 3/4; they're 6/10 and 4/10 to start

So for example, B is 4/10 • 3/9 • 2/8

and D is 1 minus the probability of no reds (or 1 minus the probability of all blue, so 1 - your answer from B)

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Probability Questions?

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