A bag contains 10 red marbles, 10 white marbles, and 10 blue marbles. What is the minimum number of marbles that need to be picked to ensure that at least 6 marbles have the same color? Marbles to pick: Ex: 20

English has 26 different letters. How many consecutive words have to be selected in a book to have at least 4 that start with the same letter? Words to select: Ex: 20

6. Rainy Days A weather forecast system predicts rain using three models: \( M_{1}, M_{2}, M_{3} \). - \( M_{1} \) is used \( 50 \% \) of the time, \( M_{2} 30 \% \), and \( M_{3} 20 \% \). - The probabilities of correctly predicting rain are \( 85 \%, 80 \% \), and \( 90 \% \) for \( M_{1}, M_{2} \), and respectively. A random day is selected. - What is the probability that rain is correctly predicted?

In a standard deck of 52 cards and 4 suits, how many cards have to be picked to be sure that at least 3 are from the same suit?

If you flip two coins, what are the possible outcomes for the combined events?

The probability of getting \( 80 \% \) or more of 28. the questions correct on a 10 - question truefalse exam merely by guessing is (A) \( 5 / 32 \) (B) \( 1 / 16 \) (C) \( 3 / 16 \) (D) \( 7 / 128 \)