Question

1. which of the following is a biased event?

the probability of pulling a red marble from a bag with 10 red marbles, 18 blue marbles and 6 green marbles.
the probability of rolling a 5 on a single die.
the probability of getting heads when flipping a coin.
the probability of drawing an ace from a standard deck of cards

Explanation:

Step1: Recall biased event definition

A biased event has unequal probabilities for outcomes (unlike fair events with equal probabilities, e.g., fair die roll, fair coin flip, standard deck draw for specific card type).

Step2: Analyze each option

• Option 1 (marble bag): Total marbles = \(10 + 18 + 6 = 34\). Probability of red: \(\frac{10}{34}\), blue: \(\frac{18}{34}\), green: \(\frac{6}{34}\). These probabilities are unequal, so the event is biased.
• Option 2 (die roll): A fair die has 6 equal - probability outcomes (\(P(5)=\frac{1}{6}\)), so it's a fair event.
• Option 3 (coin flip): A fair coin has \(P(\text{heads}) = P(\text{tails})=\frac{1}{2}\), so it's a fair event.
• Option 4 (deck of cards): A standard deck has 52 cards, 4 aces. \(P(\text{ace})=\frac{4}{52}=\frac{1}{13}\), and for other card types, the probability of drawing a non - ace is \(\frac{48}{52}\), but the probability of drawing an ace is consistent and the deck is designed to have equal probability for each card (assuming fair deck), so drawing an ace is a fair - probability event for that outcome (compared to others, but the event of drawing an ace itself has a fixed, fair - derived probability in a standard deck context).

Answer:

The probability of pulling a red marble from a bag with 10 red marbles, 18 blue marbles and 6 green marbles.