The Binomial Distribution Worksheet

**Page 1**

1.

In a family of 4 children find the probability of having atleast one boy.

a. | 0.5 | ||

b. | 0.0625 | ||

c. | 1 | ||

d. | 0.9375 |

The probability of having a boy is 0.5, so

= 1- (1)(1)(0.0625)

= 0.9375

Correct answer : (4)

2.

A group of people gathered for a small party. 15% of them are left handed, find the probability that if 6 people are chosen at random, all of them are left handed.

a. | (0.15) ^{6} | ||

b. | 0.85 | ||

c. | (0.85) ^{6} | ||

d. | 0.15 |

P (6 out of 6 are left handed) =

[Use P(

=

= (0.15)

Correct answer : (1)

3.

In a bombing attack there is 40% chance that any one bomb will strike the target. Two direct hits are required to destroy the target completely. What is the probability that the target will be destroyed, if 3 bombs are dropped?

a. | 0.4 | ||

b. | 0.56 | ||

c. | 0.288 | ||

d. | 0.96 |

P (2 out of 3 bombs strike the target) =

[Use P(

= (3) (0.16) (0.6) = 0.288

Correct answer : (3)

4.

A player has to cross 10 hurdles in a hurdle race. The probability that he will clear each hurdle is 0.83. What is the probability that he will knock down fewer than 2 hurdles?

a. | 48% | ||

b. | 50% | ||

c. | 83% | ||

d. | 80% |

Clearing a hurdle represents a success.

Probability of clearing a hurdle,

Probability of failure,

P (player knocks 0 hurdles) = P (player clears 10 hurdles) =

[Using

P (player knocks 1 hurdle) = P (player clears 9 hurdles.] =

P (player knocks fewer than 2 hurdles) = P (Player knocks fewer than 0 hurdles) + P (player knocks 1 hurdle) = 0.16 + 0.323 = 0.483 or 48.3%.

Correct answer : (1)

5.

About 75% of the seeds of a certain kind sold in a shop germinate under normal conditions. Sandra buys a packet containing 10 seeds. What is the probability that 3 of them germinate?

a. | 0.001 | ||

b. | 0.003 | ||

c. | 0.75 | ||

d. | 0.4219 |

If the seed germinates, it is considered a success,

The probability of a success,

The probability of failure,

P (3 out of 10 seeds germinate) =

[Use P (

= (120) (0.4219) (0.00006) = 0.0030

Correct answer : (2)

6.

The chance that any one telephone line is busy at a given moment of time is 0.01. What is the chance that out of 5 telephone lines, less than 3 lines are busy?

a. | 0.048 | ||

b. | .001 | ||

c. | 1 | ||

d. | 0.951 |

A line being busy represents a success,

The probability of a success,

The probability of failure,

P (0 lines are busy) =

P (1 line is busy) =

P (2 lines are busy) =

P (less than 3 lines are busy) = P (0 lines are busy) + P (1 line is busy) + P (2 lines are busy) = 0.951 + 0.048 + 0.001.

Correct answer : (3)

7.

Evaluate: _{6}C_{2} (0.4)^{2} (0.6)^{4}

a. | 0.1296 | ||

b. | 2.4 | ||

c. | 0.0207 | ||

d. | 0.3110 |

= (15) (0.16) (0.1296)

= 0.3110

Correct answer : (4)

8.

Evaluate: _{5}C_{4} (0.5)^{4} (0.5)

a. | 0.0625 | ||

b. | 0.25 | ||

c. | 0.1563 | ||

d. | 0.0313 |

= (5) (0.0625) (0.5)

= 0.1563

Correct answer : (3)

9.

Find the probability of 3 successes in 3 trials, if the probability of success on each trial is 0.8.

a. | 0.832 | ||

b. | 0.48 | ||

c. | 0.163 | ||

d. | 0.512 |

Here,

The probability of success is given by:

= (1) (0.8)

Correct answer : (4)

10.

What is the probability of 1 success in 4 trials, if the probability of success on each trial is 0.3?

a. | 0.4116 | ||

b. | 0.0756 | ||

c. | 0.0081 | ||

d. | 1.2 |

The probability of success is given by:

= (4) (0.3) (0.343)

= 0.4116

Correct answer : (1)