What is the probability of obtaining exactly 4 successes in 5 trials when the probability of success is 0.5. Round your answer to 4 decimal places.

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What is the probability of obtaining exactly 4 successes in 5 trials when the probability of success is 0.5. Round your answer to 4 decimal places.

Mathematics
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i'm not so sure but i think the probability of success is 0.5, then the probability of not success is 1-0.5=0.5 obtaining 4 successes in 5 trials = 4 successes and 1 not success so, the probability of it is 0.5^4 x 0.5 = 0.5^5 = 1/32
1/32 = 0.0312
  • Gg
I think you are right. Those happenings are independent, so we just multiply probabilities of each.

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thats actually not the answer its (5)(0.5)^4(0.5)^5-4=0.1563
  • Gg
5 times (0.5^4) times (0.5^5) -4 ?
hmm maybe because there are 5 trials, the 1/32 that i got before should be multiplied by 5, therefore the answer is the same as yours ^_^
1/32 x 5 = 0.03125 x 5 = 0.15625
yes
  • Gg
but why to multiply it by 5?
i'm also confused, but i think it's because there are 5 trials
  • Gg
but if we have 100 trials, than the possibility would be 3.1, and that is impossible, right? so, that is not the reason :)
i figured it out by the book saying this Let T denote the outcome “Tail shows” (success) and let H denote the outcome “Head shows” (failure). Using Formula (2), in which k = 1 (one success), n = 6 (the number of trials), and (the probability of success using a fair coin), we obtain
  • Gg
P= (n!/[k!(n-k)!] ) p^k * q^(n-k) use this formula. n is number of trials, k is number of successes, p is possibility of success, q=1-p :) is it ok now? :)
oh yes, combination. 5C4 0.5^4 * 0.5. thank you
  • Gg
problem solved :)

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