Probability of Drawing Same Letter
We need to find the probability that a letter drawn randomly from the word CAUSE is the same as a letter drawn randomly from the word EFFECT.
Letters in Each Word
Word 1: CAUSE
- Number of letters = 5
- Letters present: C, A, U, S, E (each appearing once)
Word 2: EFFECT
- Number of letters = 6
- Letters present: E (twice), F (twice), C (once), T (once)
Calculating Total Possible Outcomes
The total number of ways to draw one letter from CAUSE and one letter from EFFECT is the product of the number of letters in each word.
Total Outcomes = (Number of letters in CAUSE) $\times$ (Number of letters in EFFECT)
Total Outcomes = $5 \times 6 = 30$
Calculating Favorable Outcomes (Same Letter)
We need to find the pairs of letters that are the same from both words.
- Common Letters: The letters that appear in both words are 'C' and 'E'.
- Case 1: Drawing 'C'
- Ways to draw 'C' from CAUSE = 1
- Ways to draw 'C' from EFFECT = 1
- Number of pairs with 'C' = $1 \times 1 = 1$
- Case 2: Drawing 'E'
- Ways to draw 'E' from CAUSE = 1
- Ways to draw 'E' from EFFECT = 2
- Number of pairs with 'E' = $1 \times 2 = 2$
Total Favorable Outcomes = (Pairs with 'C') + (Pairs with 'E')
Total Favorable Outcomes = $1 + 2 = 3$
Determining the Probability
The probability is the ratio of favorable outcomes to total possible outcomes.
Probability = $\frac{\text{Total Favorable Outcomes}}{\text{Total Outcomes}}$
Probability = $\frac{3}{30} = \frac{1}{10}$
Important Questions from Probability (Notes)
- A box contains 20 black, 22 white, and 24 red socks. If a person draws socks at random one by one without looking, what is the minimum number of socks she must pick to be certain of having at least one pair of black socks?
The following bus schedule is seen at a bus stop located somewhere in between town A and town B.
Town A-00:10, then every 20 mins
Town B-00:15, then every 20 mins
If a person arrives at this bus stop at some random time, the probability that the next bus is for town B is- Some, but not all, faces of a six-faced cubical fair die are painted red (R) and the remaining green (G); and the die is thrown until red faces come up on top 4 times.
Consider the following sequences of colours listed left to right as they appear on the top.
A: GRRRR
B: GRGRRR
Which one of the following is true? - In a class, 40% and 20% students passed in Mathematics and Physics, respectively, and 10% students passed in both subjects. What is the probability of a randomly selected student to have passed in Physics if the student already passed in Mathematics?
- A stick of length L is broken into two pieces at random. What is the average length of the smaller piece?
