Page 350 - Start Up Mathematics_8 (Non CCE)

Number of outcomes favourable to event A m
P(A) = =
Total numberof possibble outcomes n

∑ 0 £ P(A) £ 1, i.e., probability of happening or not happening of an event lies between 0 and 1.
∑ P(A) + PA () = 1, i.e., PA () = 1 – P(A) or P(A) = 1 – PA ()

Example 1: A fair coin is tossed. What is the probability of getting a head?
Solution: When a fair coin is tossed, we get two outcomes, i.e., head (H) or tail (T).

\ Total outcomes = 2
There is only one head.
\ Favourable outcome = 1
Favourable outcome 1
Hence, probability of getting a head = =
Total outcomes 2
Example 2: A fair die is rolled once. What is the probability of getting an even number?

Solution: When a fair die is rolled once, the possible outcomes are 1, 2, 3, 4, 5 and 6.
\ Total outcomes = 6
Even numbers are 2, 4 and 6.
So, favourable outcomes = 3
Favourable outcome 3 1
Hence, probability of getting an even number = = =
Total outcomes 6 2

Example 3: A coin is tossed 50 times and head appears 30 times. What is the probability of getting a tail?
Solution: Total number of trials = 50
Number of times head appeared = 30
\ Number of times tail appeared = 50 – 30 = 20

Number of times tail appeared 20 2
Probability of getting a tail = = =
Total numberoftrials 50 5

Example 4: Two coins are tossed simultaneously. Find the probability of getting one head.

Solution: When two coins are tossed, the possible outcomes are HH, HT, TH, and TT.
Total outcomes = 4
There are 2 outcomes, namely HT and TH, which have only one head.
\ Favourable outcomes = 2
Favourable outcomes 2 1
Hence, probability of getting one head = = =
Total outcomes 4 2

Example 5: Two fair dice are rolled simultaneously. Find the probability of getting:
(a) an odd number as the sum.

(b) a doublet (i.e., same number on both dice).
(c) a multiple of 2 on one die and a multiple of 3 on the other.
(d) a total of at least 11.

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