Introduction To Probability
NIOS · Class 10 · Maths
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See them allA fair coin is tossed once. Find the probability of getting a head.
Answer
Solution: Step 1: Identify possible outcomes = {H, T} Step 2: Total outcomes = 2 Step 3: Favorable outcomes for head = 1 Step 4: P(Head) = Favorable outcomes/Total outcomes = 1/2 Answer: 1/2 or 0.5…
A die is thrown once. What is the probability of getting an even number?
Answer
Solution: Step 1: Possible outcomes = {1, 2, 3, 4, 5, 6} Step 2: Total outcomes = 6 Step 3: Even numbers = {2, 4, 6} Step 4: Favorable outcomes = 3 Step 5: P(Even) = 3/6 = 1/2 Answer: 1/2 or 0.5…
From a deck of 52 cards, one card is drawn. Find the probability of drawing a king.
Answer
Solution: Step 1: Total cards = 52 Step 2: Number of kings = 4 (one in each suit) Step 3: P(King) = Number of kings/Total cards Step 4: P(King) = 4/52 = 1/13 Answer: 1/13…
A bag contains 5 red balls and 3 blue balls. Find the probability of drawing a red ball.
Answer
Solution: Step 1: Red balls = 5, Blue balls = 3 Step 2: Total balls = 5 + 3 = 8 Step 3: Favorable outcomes (red) = 5 Step 4: P(Red) = 5/8 Answer: 5/8 or 0.625…
If P(E) = 3/7, find P(not E).
Answer
Solution: Step 1: Use the complement rule: P(E) + P(not E) = 1 Step 2: P(not E) = 1 - P(E) Step 3: P(not E) = 1 - 3/7 Step 4: P(not E) = 7/7 - 3/7 = 4/7 Answer: 4/7…
Two coins are tossed together. Find the probability of getting at least one head.
Answer
Solution: Step 1: Possible outcomes = {HH, HT, TH, TT} Step 2: Total outcomes = 4 Method 1 (Direct): At least one head = {HH, HT, TH} = 3 outcomes P(at least one head) = 3/4 Method 2 (Complement): P(a…
A die is thrown twice. Find the probability that the sum is 7.
Answer
Solution: Step 1: Total outcomes = 6 × 6 = 36 Step 2: Favorable outcomes for sum = 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) Step 3: Count = 6 outcomes Step 4: P(Sum = 7) = 6/36 = 1/6 Answer: 1/6…
From a deck of 52 cards, find the probability of drawing a red face card.
Answer
Solution: Step 1: Total cards = 52 Step 2: Red suits = Hearts and Diamonds Step 3: Face cards per suit = 3 (King, Queen, Jack) Step 4: Red face cards = 3 + 3 = 6 Step 5: P(Red face card) = 6/52 = 3/26…
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