Question

2. If two dice and one coin are rolled & tossed simultaneously than find the probability that
the coln shows head and the numbers on the top faces of the dice are not same?​

Answer 1

Answer:  For a coin, 2 possible result = { Head , Tail }

For a die ( 6 sided ), 6 possible result =1,2,3,4,5,6

Now when coin is tossed and a die is rolled simultaneously, (2×6)=12 possible result = sample spaces

{Head,1} , {Head,2} , {Head,3} , {Head,4} , {Head,5} , {Head,6} , {Tail,1} , {Tail,2} , {Tail,3} , {Tail,4} , {Tail,5} , {Tail,6}

n(s)=12

Answer 2

Therefore the probability that the coin shows the head and the numbers on the top faces of the dice are not the same is 5/12.

Given:

Two dice and one coin are rolled & tossed simultaneously.

To Find:

The probability that the coin shows the head and the numbers on the top faces of the dice are not the same.

Solution:

The given question can be solved very easily as shown below.

Let 'A' be the event of rolling 2 dice.

Let 'B' be the event of tossing a coin.

As A and B are mutually independent events,

Probability of both events happening together = P( A ∩ B ) = P( A ) × P( B )

Event-A: Not getting the same number on both the dice:

Total number of outcomes of rolling 2 dice = 6² = 36

The ways in which both dice show the same number = (1,1), (2,2), (3,3), (4,4), (5,5), (6,6)

The number of ways both dice show the same number = 6

Number of ways in which both dice do not show the same number = 36-6 = 30 ways

So the number of favorable outcomes = 30

⇒ Probability of not getting the same number on both the dice = ( number of favorable outcomes )/( number of total outcomes )

⇒ Probability of not getting the same number on both the dice = 30/36 = 5/6

⇒ P(A) = 5/6

Event-B: Getting the head on coin:

The number of total outcomes = 2 ( Head or Tail )

Number of favorable outcomes = 1 ( Head )

⇒ Probability of getting head = ( number of favorable outcomes )/( number of total outcomes )

⇒ Probability of getting head = 1/2

⇒ P(B) = 1/2

Now, the probability that the coin shows the head and the numbers on the top faces of the dice are not the same is given by,

⇒ P( A ∩ B ) = P( A ) × P( B ) = (5/6) × (1/2) = 5/12

Therefore the probability that the coin shows the head and the numbers on the top faces of the dice are not the same is 5/12.

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