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When a certain coin is flipped, the probability of heads is
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19 Nov 2019, 11:37
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When a certain coin is flipped, the probability of heads is 0.5. If the coin is flipped 6 times, what is the probability that there are exactly 3 heads?
Re: When a certain coin is flipped, the probability of heads is
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08 Nov 2020, 20:06
1
So there should be 3 heads and 3 tails now order does matter here like HHHTTT is same as HTHTHT (both have exactly 3 heads) - the number of ways of selecting 6 positions of possibilities are 6! but there should be 3 heads and 3 tails due to repetition, thus the number of ways would be 6!/ 3! * 3! = 20 ways in which we'll get exactly 3 heads - total number of outcomes = 2^n ( 2 because there are only 2 possibilities heads and tails ) n = 6 ( since there are 6 tosses) the total number of outcomes are 2^6= 64
Re: When a certain coin is flipped, the probability of heads is
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14 Oct 2022, 09:51
1
Given that When a certain coin is flipped, the probability of heads is 0.5 and the coin is flipped 6 times. And we need to find what is the probability that there are exactly 3 heads?
Now there are six places to fill as shown below
_ _ _ _ _ _
We need to get 3 Heads and 3 Tails. Now lets find out the slots out of these 6 in which 3 heads will go.
We can find that using 6C3 = \(\frac{6!}{3!*(6-3)!}\) = \(\frac{6!}{3!*3!}\) = \(\frac{6*5*4*3*2*1}{3*2*1*3*2*1}\) = 20 ways
Now, in the remaining slots we will have Tails. So we can get 3H and 3T in 20 ways
We know that probability of getting a head, P(H), = Probability of getting a Tail, P(T) = \(\frac{1}{2}\)
=> Probability of getting 3H and 3T = Number of ways * P(H) * P(H) * P(H) * P(T) * P(T) * P(T) = 20 * \(\frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2} * \frac{1}{2}\) = \(\frac{5}{16}\)
So, Answer will be C Hope it helps!
Watch the following video to learn How to Solve Probability with Coin Toss Problems
gmatclubot
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