25.17
11. Three biased coins were tossed 800 times simultaneously. The outcomes are given in
the following table:
Outcome: No head One head Two head
Frequency: 120
280 x
If the probability of occurrence of two heads is thrice that of all heads, then the value
of x is
(a) 150
(b) 240
(c) 300
(d) 360
Answers
Answer:
Let E9 = event of getting 1 head and 1 tail. Then, E9 = {HT, TH } and, therefore, n(E9) = 2. Therefore, P(getting 1 head and 1 tail) = P(E9) = n(E9)/n(S)= 2/4 = 1/2.
Given : Three biased coins were tossed 800 times simultaneously. The outcomes are given . probability of occurrence of two heads is thrice that of all heads.
No head 120
One head 280
Two Head x
To find : Value of x
Solution:
No head 120
One head 280
Two Head x
Three Head y
Total = 800
probability of occurrence of two heads is thrice that of all heads
=> x/800 = 3 * y/800
=> x = 3y
=> y = x/3
No head 120
One head 280
Two Head x
Three Head x/3
Total = 800
120 + 280 + x + x/3 = 800
=> 4x/3 = 400
=> x = 300
value of x is 300
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