Six coin arc tossed simultaneously. Find the probability of getting(i)

1.	Six coin arc tossed simultaneously. Find the probability of getting(i) no head(ii) at least one head.
Answer» Let P = Probability of getting a head in the single toss of coin = 1/2 and q = Probability of not getting a head = 1 - P = 1 - (1/2) = 1/2 Let number of successes in the experiment be 'x' So, x can take the value 0,1,2,3,4,5,6 Also, x = no. of trial = 6 (i) P(no head) = P(x = 0) ⁶C₀(1/2)⁰ (1/2)^{(6 - 0)} = 1/64 (ii) P(at least one hand) = 1 - P(no head) = 1 - (1/64) = 63/64

Six coin arc tossed simultaneously. Find the probability of getting(i) no head(ii) at least one head.

Answer»

Let P = Probability of getting a head in the single toss of coin = 1/2 and q = Probability of not getting a head

= 1 - P = 1 - (1/2) = 1/2

Let number of successes in the experiment be 'x'

So, x can take the value 0,1,2,3,4,5,6

Also, x = no. of trial = 6

(i) P(no head) = P(x = 0)

⁶C₀(1/2)⁰ (1/2)^{(6 - 0)} = 1/64

(ii) P(at least one hand) = 1 - P(no head) = 1 - (1/64) = 63/64