The probability of getting a “head” in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a “head” is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is __________
Correct Answer
Solution & Step-by-step Explanation
In the range: 0.07 - 0.08
Given:
P(Head) = 0.3 = p and
P(Tail) = 0.7 = q
The probability of getting a "head" for the first time in the fifth toss means that "tails" have appeared in the first four tosses.
∴ The required probability will be:
P = P(Tail) .P(Tail). P(Tail). P(Tail). P(Head)
P = (0.7)⁴ (0.3) = 0.07203
Given:
P(Head) = 0.3 = p and
P(Tail) = 0.7 = q
The probability of getting a "head" for the first time in the fifth toss means that "tails" have appeared in the first four tosses.
∴ The required probability will be:
P = P(Tail) .P(Tail). P(Tail). P(Tail). P(Head)
P = (0.7)⁴ (0.3) = 0.07203