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If A Coin Is Tossed 5 Times, Using Binomial Distribution

If a coin is tossed 5 times, using binomial distribution find the probability of:

(a) Exactly 2 heads

(b) At least 4 heads

SOLUTION:

(a) According to the problem:

Number of trials: n = 5

The probability of head: p = 1/2 and the probability of tail, q =1/2

For exactly 2 heads ( x = 2 ) = 5C2 . (1/2)2 . (1/2)5-2

= 5! / 2!3! x ¼ x 1/8

= 10 x 1/32

= 5/16

Answer; P ( x = 2 ) = 5/16.

 

(b) Number of trials; n = 5

The probability of head: p = 1/2 and the probability of tail, q =1/2

At least 4 heads (x > 4) = P ( x = 4 ) + P ( x = 5 )

P ( x = 4 ) = 5C4 . (1/2)4 . (1/2)5-4

P ( x = 4 ) = 5! / 4!1! x 1/16 x ½

P ( x = 4 ) =  5/32

P ( x = 5 ) =  5C5 . (1/2)5 . (1/2)5-5

P ( x = 5 ) = 5! / 5!0! x 1/32 x 1

P ( x = 5 ) = 1/32

 

P ( x > 4 ) = 5/32 + 1/32 = 6/32 = 3/16

Answer; P ( x > 4 ) = 3/16

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