Solved Questions on Probability
1. A six-sided dice was rolled 1500 times and the number of times each outcome (1, 2, 3, 4, 5 and 6) occurred is provided below:
|
Outcome
|
1
|
2
|
3
|
4
|
5
|
6
|
|
Frequency
|
123
|
321
|
235
|
315
|
186
|
320
|
What is the probability of the outcome 4 not happening on the dice?
a) 0.21
b) 41
c) 59
d) 79
Answer:d) 0.79
Explanation:
n(S) = Total frequency = 1500
n(E) = Frequency at 4 occurs on the dice = 315
Probability of the outcome 4 happening on the dice is:
P(E) = n(E)/n(S) = 315/1500 = 0.21
Probability of the outcome 4 not happening on the dice is:
P( E′) = 1 − P(E) = 1 − 0.21 = 0.79
2. A plastic bottle factory manufactures small and large sized bottles. Small-sized bottles include 50 mL, 100 mL, 200 mL and 250 mL. Large-sized bottles include 500 mL, 1000 mL and 500 mL. The manufacturing of bottles of different capacities per day is shown as follows:
|
Capacity of bottle
|
50 mL
|
100 mL
|
200 mL
|
250 mL
|
500 mL
|
1000 mL
|
5000 mL
|
|
Number of bottles
|
780
|
1030
|
860
|
735
|
786
|
544
|
765
|
What is the probability of manufacturing large-sized bottles?
a) 0.38
b) 0.48
c) 0.62
d) 0.52
Answer:a) 0.38
Explanation: n(S) = Total bottles manufactured per day
= 780 + 1030 + 860 + 735 + 786 + 544 + 765
= 5500
n(E) = Total large-sized bottles manufactured per day
= 786 + 544 + 765
= 2095
Probability of manufacturing large-sized bottles is:
P(E) = n(E)/n(S) = 2095/5500 = 0.38
3. What is the probability of at least one tail when three coins are tossed simultaneously?
a) 0.125
b) 0.375
c) 0.625
d) 0.875
Answer:d) 0.875
Explanation: Total outcomes, S = {HHH, TTT, HHT, TTH, HTT, THH, THT}
n(S) = Number of total outcomes = 8
Favourable outcomes to get at least one tail,
E = {TTT, HHT, TTH, HTT, THH, THT}
n(E) = Favourable outcomes to get at least one tail = 7
Probability of at least one tail when three coins are tossed simultaneously is:
P(E) = n(E)/n(S) = 7/8 = 0.875
4. A carton contains 25 balls bearing numbers: 1, 2, 3, 4, …….., 25. A ball is drawn at random from the carton. What is the probability of the number divisible by 3 or 7 on the balls?
a) 1/5
b) 2/
c) 3/5
d) 4/5
Answer:b) 2/5
Explanation: S = Numbers on the balls ={1, 2, 3, ……………., 25}
n(S) = 25
E = Numbers divisible by 3 or 7 = {3, 6, 7, 9, 14, 12, 15, 18, 21, 24}
n(E) = 10
Probability of at least one tail when three coins are tossed simultaneously is:
P(E) = n(E)/n(S) = 10/25 = 2/5
5. In a board game, there is a spinner divided into 12 equal sections: Black, Grey, Red, Blue, Orange, White, Brown, Pink, Yellow, Green, Purple and Silver. If you spin the spinner, what is the probability of it not landing on Green?
a) 8.33%
b) 28.33%
c) 71.67%
d) 91.67%
Answer:d) 91.67%
Explanation: n(S) = Total number = 12
n(E) = 1
Probability of spinner landing on Green is:
P(E) = n(E)/n(S) = 1/12 = 1/12 × 100 = 8.33%
Probability of spinner not landing on Green is:
P( E′) = 1 − P(E) = 100% − 8.33% = 91.67%
