Probability sums with question and answer

Probability sums with question and answer

Introduction

Probability sums are not only mathematical problems, it is one kind of brain game that makes one think about the possibilities. Which is useful to improve individual aptitude skills. This article will be helpful for those who are preparing for the civil service examinations like TNPSC group exams, TET, RRB, UPSC, Banking exams, and so on. We have listed the probability sums with solutions, start preparing for your exams!

Probability formulas and sums are available in the previous article. Click and view here!

6. Two dice are thrown simultaneously. What is the probability of getting two numbers whose sum equal to 10?

Answer:

Explanation:

In a simultaneous throw of two dice, we have n ( S ) = ( 6 × 6 ) = 36

Let E = event of getting two numbers whose sum is 10

Then E = { ( 4, 6 ), ( 5, 5 ), ( 6, 4 ) ]

n ( E ) = 3

P ( E ) = n ( E ) / n ( S )

= 3 / 36

= 1 / 12

The probability of getting two numbers whose sum is equal to 10 is 1 / 12.

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7. What is the probability of getting a number less than 5 when a die is rolled?

Answer:

Explanation:

In a throw of single dice, we have n ( S ) = ( 1, 2, 3, 4, 5, 6 )

= 6

Let E = event of getting a number less than 5 Then E = { 1, 2, 3, 4 ]

n ( E ) = 4

P ( E ) = n ( E ) / n ( S )

= 4 / 6

= 2 / 3

The probability of getting a number less than 5 is 2 / 3.

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8. A dice is thrown. What is the probability that the number shown in the dice is divisible by 2?

Answer:

Explanation:

In a throw of single dice, we have n ( S ) = ( 1, 2, 3, 4, 5, 6 )

= 6

Let E = event of getting a number is divisible by 2 Then E = { 2, 4, 6 ]

n ( E ) = 3

P ( E ) = n ( E ) / n ( S )

= 3 / 6

= 1 / 2

The probability of getting a number is divisible by 2 is 1 / 2.

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9. Three unbiased coins are tossed. What is the probability of getting two tails?

Answer:

Explanation

Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

n ( S ) = 8

Let E = Event of getting two tails

Then E = {TTT, TTH, THT, HTT}

n ( E ) = 4

P ( E ) = n ( E ) / n ( S )

= 4 / 8

= 1 / 2

The probability of getting two tails is 1 / 2.

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10. Two dice are thrown simultaneously. What is the probability of getting two numbers whose product is odd?

Answer:

Explanation:

In a simultaneous throw of two dice, we have n ( S ) = ( 6 × 6 )

= 36

Let E = Event of getting two numbers whose product is odd

Then E = { ( 1, 1 ), ( 1, 3 ), ( 1, 5 ), ( 3, 1 ), ( 3, 3 ), ( 3, 5 ), ( 5, 1 ), ( 5, 3 ), ( 5, 5 ) }

n ( E ) = 9

P ( E ) = n ( E ) / n ( S )

= 9 / 36

= 1 / 4

The probability of getting two numbers whose product is odd is 1 / 4.

Conclusion

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