Question:

A bag contains n+1n + 1 coins. It is known that one of these coins shows heads on both sides, whereas the other coins are fair. One coin is selected at random and tossed. If the probability that toss results in heads is 712\frac{7}{12}, then the value of nn is.

Updated On: Sep 3, 2024
  • 3
  • 4
  • 5
  • None of these
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

Let E1E_1 denote the event "a coin with head on both sides is selected" and E2E_2 denotes the event " a fair coin is selected".
Let AA be the event " he toss, results in heads".
P(E1)=1n+1,P(E2)=nn+1\therefore P\left(E_{1}\right) = \frac{1}{n+1} , P\left(E_{2}\right) = \frac{n}{n+1} and
P(AE1)=1,P(AE2)=12 P\left(\frac{A}{E_{1}} \right) = 1, P\left(\frac{A}{E_{2}}\right) = \frac{1}{2}
P(A)=P(E1)P(AE1)+P(E2)P(AE2) \therefore P\left(A\right) =P\left(E_{1}\right)P\left(\frac{A}{E_{1}}\right) + P\left(E_{2}\right)P\left(\frac{A}{E_{2}}\right)
712=1n+1×1+nn+1×12 \Rightarrow \frac{7}{12} = \frac{1}{n +1} \times1 + \frac{n}{n+1} \times \frac{1}{2}
14n+14=24+12n\Rightarrow 14n +14 = 24 +12n
n=5 \Rightarrow n = 5
Was this answer helpful?
0
1

Concepts Used:

Random Experiments

An Experiment is the activity that produces a result or an outcome. It is an element of uncertainty as to which it occurs when we perform an activity or experiment. Normally we get a different number of outcomes from an experiment. However, when an experiment satisfies the following two conditions, it is known as random experiment.

  • It has more than one possible outcome.
  • It is not possible to predict the outcome in advance.

On the basis of random experiment we can identify whether the given experiment is random or not. Let’s check with the help of example which is a random experiment and which is not.

Question: Using a calculator, divide 36 by 4. Now check, whether it is a random experiment or not.

Solution:

  • This activity can be repeated under identical conditions though it has only one possible result.
  • The outcome is always 9, which means we can predict the outcome each time we repeat the operation.

The given activity is not a random experiment.