You toss a fair coin four times: A: what is the probability of that you observe

Question

You toss a fair coin four times:
A: what is the probability of that you observe exactly two heads?

B: what is the probability of at least three heads?

C: given that you have observed at least one heads, what is the probability that you observe at least two heads?

Q1: 20 Points You toss a fair coin four times: A: what is the probability of that you observe exactly two heads? B: what is the probability of at least three heads? C: given that you have observed at least one heads, what is the probability that you observe at least two heads?

Explanation / Answer

A: P(2 heads) = 4C2 x (1/2)2 x (1/2)2 = 0.375

B: P(at least 3 heads) = P(3 heads) + P(4 heads)

= 4C3 x (1/2)4 + (1/2)4

= 0.25 + 0.0625

= 0.3125

C: P( 2 heads | at least 1 head) = P(2 heads)/P(at least 1 head)

= 0.375/(1 - 0.54)

= 0.4

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