Explanation
Step -1: Finding the probability of getting head in each toss.
Let a coin is tossed n times.
The probability of getting head in one trial, p=12.
Step -2: Finding the number of times a coin is tossed.
Probability of getting at least one head=P(X≥1)
=1−P(X=0)
=1−nC0(1−p)n
=1−(1−12)n
=1−12n≥0.8 (Given)
⇒12n≤1−0.8
⇒12n≤0.2
When n=1,
12n=12=0.5>0.2
When n=2,
12n=122=0.25>0.2
When n=3,
12n=123=0.125<0.2
∴n should be 3.
Hence, correct option is D.
Step -1: Finding the Probability of success and failure
Let a step forward be a success and a step backward be a failure.
Then, the probability of success in one step
⇒P = 0.4 = 25
The probability of failure in one step = Q = 0.6 = 35
In 11 steps he will be one step away from the staring point if the numbers of successes
and failure differ by 1.
So, the number of successes = 6
The number of failures = 5
or the number of successes = 5,
The number of failures = 6
Step -2: Finding required probability
∴The required probability = 11C6P6Q5+11C5P5Q6
=11C6(25)6.(35)5+11C5(25)5.(35)6
=11!6!.5!.(25)5.(35)5.{25+35}
=11.10.9.8.7120.25.35510
=462×(625)5
=0.368
Hence, correct answer is option A
Please disable the adBlock and continue. Thank you.